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I've had an idea for a post like this rattling in my head for a while. I thought we should have some sort of resource and discussion on jet engines, how they work, and what the various figures of merit are.
For simplicity, I'll talk about thrust turbines in aircraft, although there are a whole host of important gas turbine applications, like the power gas turbines used in helicopters, tanks and ships, to say nothing of steam turbines.
This is a representative schematic of a turbojet. For some reason, all schematic diagrams of turbojet engines show axial compressors, even though centrifugal compressors are still common.
Air flows in through the inlet. Rotating compressor blades, attached to a central shaft or spool and stationary stator blades compress air. This compressed air is fed to the combustors, where fuel is burned to heat the air (in principle heat energy could be added by means other than combustion, as in a nuclear gas turbine). This hot air is then fed to the turbine section where it spins turbine blades, which are mounted to the same shaft as the compressor blades. Some of the energy from the hot gas is used to turn the turbines, but the rest rushes out the back where a nozzle extracts maximum thrust from it.
For best performance, the pressure ratio, that is, the ratio of the pressure of air in the final stage of the compressor to free atmospheric air, should be as high as possible. Pressure ratio is related both to specific power (how much thrust you can get per kilogram of engine) and efficiency (how much thrust you can get per kilogram of fuel):
This chart shows the idealized relationship between efficiency (Y axis) and pressure ratio (X axis). Higher is better, but after a certain point there are somewhat diminishing returns.
Pressure ratio has risen dramatically since the development of the first gas turbines. The Jumo 004 in the ME-262 had a pressure ratio of 4:1 or so, while the Trent 900 in the Airbus A380 manages nearly 40:1! Civil turbine engines can support somewhat higher compression ratios, since airliners cruise for long periods of time at a given altitude and speed. Military aircraft have fighter jocks shoving the throttles this way and that and operate over a wide range of altitudes and speeds, so there needs to be some more wiggle room. Most contemporary fighter aircraft engines have pressure ratios between 20:1 and 30:1.
Additionally, contrary to what the diagram above shows, in most thrust jet engines, not all of the air from the compressor goes through the core:
A portion of the air bypasses the core, and simply joins the air that went through the core in the nozzle. The bypass ratio is the ratio (in mass per second) of air that goes around the core relative to the air going through the core. An engine with any amount of bypass air is called a turbofan, while one without is a turbojet.
This bypass air serves two purposes. The first is that because it did not go through the core and past the combustor, it is relatively cool and therefore helps to cool the engine nozzle. The variable geometry nozzles (overlapping metal flower looking thingies) used on modern fighter aircraft require some amount of bypass air to maintain structural integrity:
The second purpose of bypass air is to generate thrust. At low altitudes and airspeeds, bypass air is a more efficient way to generate thrust than core air.
Airliner engines were initially turbojets, but these quickly sprouted bypass ducts. Airliner engines currently have much higher bypass ratios than fighter aircraft engines, as again, fighter aircraft are expected to operate at least occasionally at speeds and altitudes where high bypass is not efficient. Additionally, higher bypass ratios make engines wider, and therefore draggier, as well as less responsive to throttle input. The Trent 900 has a bypass ratio of 8.5:1, while the RB199 has the highest bypass ratio of any fighter engine at 1.1:1. The F119 in the F-22 raptor has an unusually low bypass ratio of .2:1, making it practically a pure turbojet with just enough bypass air for nozzle cooling only. It is also possible to make variants of engines that incorporate existing core designs, but have a different bypass ratios. The F135 in the JSF, for example, has essentially the same core as the F119, but has a bypass ratio of .55:1. Because the JSF does not supercruise, it is worth trading off some performance at supersonic speeds in favor of efficiency in subsonic.
The turbine section of the engine is the most demanding in terms of materials science. The higher the temperature at which the turbine operates, the more efficient and power-dense the engine can be. The demands of higher and higher performance have long since pushed temperatures past the operating range of steels, so now turbine blades in top of the line engines are made of magical nickel alloys with magical microstructure, cooling air actively circulated inside of them, and magical ceramic coatings:
The expertise to make high performance gas turbine blades is kept secret and restricted to a handful of companies in the world's richest nations.
Finally, the hot air from the turbine and the bypass air (if any) are mixed and expelled out of a nozzle. Because they operate within a narrow band of altitudes and speeds, simple, fixed-geometry nozzles are acceptable for airliners. Combat aircraft typically need complex, actively cooled variable-geometry nozzles. The most recent development in this area has been the so-called 2D, or rectangular nozzle, as seen in the F119 engine:
These nozzles are heavier, and sacrifice some efficiency (not that it really matters; the F119 is a mighty beast with thrust to spare) in exchange for lower radar and infra-red cross section. Additionally, the F119 can point the thrust up or down by twenty degrees, which enhances the agility of the F-22, especially at high altitudes.
Most combat aircraft engines feature afterburners. An afterburner dumps additional fuel into the hot air aft of the turbine stage. Afterburners provide a dramatic increase in thrust, usually doubling it, but have a disproportionate increase in fuel consumption, usually increasing it by a factor of seven or so.

Thinking about the effect of a heavier boolit on the combustion, it reminded me of what my thermo lecturer was talking about with the idealised otto cyle and diesel cycle - modelling the combustion as simple heat addition, a heavier boolit will get more PdV work.
So, the otto cycle is more efficient than a diesel cycle ceteris paribus - this is because the ignition of the fuel is so quick it's kinda like isochoric heat addition (i.e. constant volume), whereas diesels are limited by the time it takes to inject the fuel* so are better approximated by isobaric heat addition (constant pressure, so with volume increasing). Since some travel is taking place in the diesel cycle before all the heat is added, there's less area under the P-V diagram so less work is done.
*according to my lecturer, non-direct injection diesels are not halal
Something similar will happen with a heavier boolit - it will have moved less before all the propellant is combusted, so it's closer to the ideal of holding the bullet in place until all the propellant has combusted to maximise PdV work*. A light boolit, OTOH, will have moved down the tube more when the pressure in the chamber was low, so doesn't get as much work done on it. The rate of combustion is probably proportional to pressure and temp as well, giving an even more pronounced effect. All this is happening completely separate to the not-quasi-equilibrium thingy with the ratio of propellant gas speeds and boolit speed - that reduces efficiency towards the end of the barrel, whereas this reduces efficiency near the chamber where velocities are much lower
*maximum pressure limits are for wusses